Calculus Optimization - Point on graph closest to given point












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Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?










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    Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?










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      $begingroup$


      Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?










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      Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?







      calculus optimization






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      edited 1 hour ago









      dmtri

      1,7712521




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      asked 2 hours ago









      Julian CallegariJulian Callegari

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          1 Answer
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          $begingroup$

          HINT



          If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
          $$
          D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
          $$

          Can you simplify and minimize $D(x)$?






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            1 Answer
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            1 Answer
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            active

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            active

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            3












            $begingroup$

            HINT



            If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
            $$
            D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
            $$

            Can you simplify and minimize $D(x)$?






            share|cite|improve this answer









            $endgroup$


















              3












              $begingroup$

              HINT



              If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
              $$
              D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
              $$

              Can you simplify and minimize $D(x)$?






              share|cite|improve this answer









              $endgroup$
















                3












                3








                3





                $begingroup$

                HINT



                If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
                $$
                D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
                $$

                Can you simplify and minimize $D(x)$?






                share|cite|improve this answer









                $endgroup$



                HINT



                If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
                $$
                D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
                $$

                Can you simplify and minimize $D(x)$?







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 1 hour ago









                gt6989bgt6989b

                35.6k22557




                35.6k22557






















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